What frustrates me most about current state of banking apps is a complete isolation and not much of flexibility. There are a lot of trivial things (or so I think) that could be achieved easily in a modern app. What I would need is ability to create transaction rules. For example:
When you get a salary transaction from my employer, contribute 5% to my savings account A, and 4% to my savings account B (on Mondo). Create those accounts if none exists.
There should be ability to create as many accounts as needed - even if those accounts are virtual and are only accessible within Mondo app. For each account you could again specify things like:
Every month if there is at least 100£ on my savings account C, contribute 20£ to Red Cross.
All those things should be IFTTT style user configurable and easily changeable without annoying calls to bank or other nonsense. Potentially you could outsource rules creation to the API and allow 3rd party app to import rule profiles into your Mondo profile.
Also, think about Goals. You could allow setting something like:
Help me reach a safe buffer which equals 3 months of my current salary, or Help me save for a holidays in Iceland
This would allow user to see how far is the progress and make adjustments.
Somehow I feel part of these ideas could already be implemented with the current API.